1SLANHS(1) LAPACK auxiliary routine (version 3.1) SLANHS(1)
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6 SLANHS - the value of the one norm, or the Frobenius norm, or the
7 infinity norm, or the element of largest absolute value of a Hessenberg
8 matrix A
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11 REAL FUNCTION SLANHS( NORM, N, A, LDA, WORK )
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13 CHARACTER NORM
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15 INTEGER LDA, N
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17 REAL A( LDA, * ), WORK( * )
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20 SLANHS returns the value of the one norm, or the Frobenius norm, or
21 the infinity norm, or the element of largest absolute value of a
22 Hessenberg matrix A.
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26 SLANHS returns the value
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28 SLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
29 (
30 ( norm1(A), NORM = '1', 'O' or 'o'
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32 ( normI(A), NORM = 'I' or 'i'
33 (
34 ( normF(A), NORM = 'F', 'f', 'E' or 'e'
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36 where norm1 denotes the one norm of a matrix (maximum column sum),
37 normI denotes the infinity norm of a matrix (maximum row sum) and
38 normF denotes the Frobenius norm of a matrix (square root of sum of
39 squares). Note that max(abs(A(i,j))) is not a consistent matrix
40 norm.
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44 NORM (input) CHARACTER*1
45 Specifies the value to be returned in SLANHS as described
46 above.
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48 N (input) INTEGER
49 The order of the matrix A. N >= 0. When N = 0, SLANHS is set
50 to zero.
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52 A (input) REAL array, dimension (LDA,N)
53 The n by n upper Hessenberg matrix A; the part of A below the
54 first sub-diagonal is not referenced.
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56 LDA (input) INTEGER
57 The leading dimension of the array A. LDA >= max(N,1).
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59 WORK (workspace) REAL array, dimension (MAX(1,LWORK)),
60 where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
61 enced.
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65 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006 SLANHS(1)